Joe has decided to invest to help with his retirement savings. How much would he need to invest to have \( \$ 136900 \) after 20 years, assuming an interest rate of \( 3.46 \% \) compounded monthly? Round to the nearest

To find out how much Joe needs to invest, we can use the future value formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the future value (\$136,900), - \( P \) is the principal amount (the initial investment), - \( r \) is the annual interest rate (3.46% or 0.0346), - \( n \) is the number of times that interest is compounded per year (12 for monthly), - \( t \) is the number of years the money is invested (20). Rearranging this formula to solve for \( P \): \[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \] Plugging in the numbers: \[ P = \frac{136900}{\left(1 + \frac{0.0346}{12}\right)^{12 \times 20}} \] Calculating the value gives Joe the amount he needs to invest, which will be approximately \$19,154 when rounded to the nearest dollar. To maximize Joe's returns, he could also explore other investment options like stocks or bonds that might offer higher interest rates, albeit with varying levels of risk. Diversifying his portfolio can offer stability while still aiming for that golden retirement fund! It's also key that Joe keeps an eye on fees associated with investments, as they can eat into those hard-earned savings. Looking for low-cost index funds or ETFs can be a smart move; every dollar saved on fees is a dollar working for his future!